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Abstract

Many numerical algorithms have error bounds that depend on some user provided input.  For example, the error in a numerical method for solving a differential equation is bounded in terms of the step-size h, and so the user may change the step-size h until a desired accuracy is attained.  Although useful, these error bounds do not take account of computational efficiency.  For example, a numerical method for solving a differential equation may have a very impressive bound with respect to step size h, but may require significantly more computational effort than other methods with less impressive error bounds.  The field of scientific computing is a rich source of algorithms such as these, for example the numerical solution of differential equations, the numerical solution of linear systems, and interpolation of functions.  The aim of this project is to work with a variety of algorithms for solving a given problem, and to assess the computational efficiency of these algorithms.